{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ***Introduction to Radar Using Python and MATLAB***\n",
    "## Andy Harrison - Copyright (C) 2019 Artech House\n",
    "<br/>\n",
    "\n",
    "# Binary (M of N) Integration\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Binary integration is another form of noncoherent integration, often referred to as $M$ of $N$ detection, and is shown in Figure 6.10.  In this form of integration, each of the $N$ return signals is passed separately through the threshold detector.  There must be $M$ individual detection declarations in order for a target to be declared as present.  Binary integration is somewhat simpler to implement than coherent and noncoherent integration.\n",
    "\n",
    "The probability of detection for binary integration is written as (Equation 6.24)\n",
    "\n",
    "$$\n",
    "    P_{{MN}} = \\sum_{k=M}^N C_{{kN}}\\cdot p^k\\cdot (1-p)^{N-k},\n",
    "$$\n",
    "\n",
    "where $p$ is the single pulse probability of detection, and $C_{{kN}}$ is the binomial coefficient given by (Equation 6.25)\n",
    "\n",
    "$$\n",
    "    C_{{kN}} = \\frac{N!}{k!\\, (N-k)!}.\n",
    "$$\n",
    "\n",
    "Similarly, the probability of false alarm is (Equation 6.26)\n",
    "\n",
    "$$\n",
    "    F_{{MN}} = \\sum_{k=M}^N C_{{kN}}\\cdot f^k\\cdot (1-f)^{N-k},\n",
    "$$\n",
    "\n",
    "where $f$ is the single pulse probability of false alarm. For binary integration, some optimum value of $M$ exists that minimizes the required signal-to-noise ratio for given probabilities of detection and false alarm, and a given $N$.  Richards  provides a nice approximation for $M$ for various target fluctuations, which is given here as (Equation 6.27)\n",
    "\n",
    "$$\n",
    "    M_{{opt}} = 10^{\\beta}\\, N^{\\alpha},\n",
    "$$\n",
    "\n",
    "where the values for $\\alpha$ and $\\beta$ are given in Table 6.3.\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Begin by getting the library path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import lib_path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the start and end signal to noise ratio (dB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "snr_start = 3.0\n",
    "\n",
    "snr_end = 20.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert to linear units and create an array using `linspace` from `scipy`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import linspace\n",
    "\n",
    "snr = 10.0 ** (linspace(snr_start, snr_end, 200) / 10.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the probability of false alarm, and the parameters **m** and **n**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pfa = 1e-6\n",
    "\n",
    "m = 3\n",
    "\n",
    "n = 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the probability of detection for each signal to noise ratio using the `probability_of_detection` routines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Libs.detection import binary_integration, single_pulse\n",
    "\n",
    "pd = [binary_integration.probability_of_detection(m, n, single_pulse.pd_rayleigh(isnr, pfa)) for isnr in snr]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display the probability of detection for binary integration using the `matplotlib` routines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from numpy import log10\n",
    "\n",
    "\n",
    "\n",
    "# Set the figure size\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (15, 10)\n",
    "\n",
    "\n",
    "\n",
    "# Display the results\n",
    "\n",
    "plt.plot(10.0 * log10(snr), pd, '')\n",
    "\n",
    "\n",
    "\n",
    "# Set the plot title and labels\n",
    "\n",
    "plt.title('Binary Integration (M of N)', size=14)\n",
    "\n",
    "plt.xlabel('Signal to Noise (dB)', size=12)\n",
    "\n",
    "plt.ylabel('Probability of Detection', size=12)\n",
    "\n",
    "\n",
    "\n",
    "# Set the tick label size\n",
    "\n",
    "plt.tick_params(labelsize=12)\n",
    "\n",
    "\n",
    "\n",
    "# Turn on the grid\n",
    "\n",
    "plt.grid(linestyle=':', linewidth=0.5)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
